Search results for: Lyapunov Functionals.
120 Augmented Lyapunov Approach to Robust Stability of Discrete-time Stochastic Neural Networks with Time-varying Delays
Authors: Shu Lü, Shouming Zhong, Zixin Liu
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In this paper, the robust exponential stability problem of discrete-time uncertain stochastic neural networks with timevarying delays is investigated. By introducing a new augmented Lyapunov function, some delay-dependent stable results are obtained in terms of linear matrix inequality (LMI) technique. Compared with some existing results in the literature, the conservatism of the new criteria is reduced notably. Three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed method.
Keywords: Robust exponential stability, delay-dependent stability, discrete-time neural networks, stochastic, time-varying delays.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1427119 Influence of Adaptation Gain and Reference Model Parameters on System Performance for Model Reference Adaptive Control
Authors: Jan Erik Stellet
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This article presents a detailed analysis and comparative performance evaluation of model reference adaptive control systems. In contrast to classical control theory, adaptive control methods allow to deal with time-variant processes. Inspired by the works [1] and [2], two methods based on the MIT rule and Lyapunov rule are applied to a linear first order system. The system is simulated and it is investigated how changes to the adaptation gain affect the system performance. Furthermore, variations in the reference model parameters, that is changing the desired closed-loop behaviour are examinded.Keywords: Adaptive control systems, Adaptation gain, MIT rule, Lyapunov rule, Model reference adaptive control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2214118 A C1-Conforming Finite Element Method for Nonlinear Fourth-Order Hyperbolic Equation
Authors: Yang Liu, Hong Li, Siriguleng He, Wei Gao, Zhichao Fang
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In this paper, the C1-conforming finite element method is analyzed for a class of nonlinear fourth-order hyperbolic partial differential equation. Some a priori bounds are derived using Lyapunov functional, and existence, uniqueness and regularity for the weak solutions are proved. Optimal error estimates are derived for both semidiscrete and fully discrete schemes.
Keywords: Nonlinear fourth-order hyperbolic equation, Lyapunov functional, existence, uniqueness and regularity, conforming finite element method, optimal error estimates.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1877117 Self-Organizing Control Systems for Unstable and Deterministic Chaotic Processes
Authors: M. A. Beisenbi, N. M. Kissikova, S. E. Beisembina, S. T. Suleimenova, S. A. Kaliyeva
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The paper proposes a method for constructing a self-organizing control system for unstable and deterministic chaotic processes in the class of catastrophe “hyperbolic umbilic” for objects with m-inputs and n-outputs. The self-organizing control system is investigated by the universal gradient-velocity method of Lyapunov vector-functions. The conditions for self-organization of the control system in the class of catastrophes “hyperbolic umbilic” are shown in the form of a system of algebraic inequalities that characterize the aperiodic robust stability in the stationary states of the system.
Keywords: Gradient-velocity method of Lyapunov vector-functions, hyperbolic umbilic, self-organizing control system, stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 438116 Design of an Augmented Automatic Choosing Control with Constrained Input by Lyapunov Functions Using Gradient Optimization Automatic Choosing Functions
Authors: Toshinori Nawata
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In this paper a nonlinear feedback control called augmented automatic choosing control (AACC) for a class of nonlinear systems with constrained input is presented. When designed the control, a constant term which arises from linearization of a given nonlinear system is treated as a coefficient of a stable zero dynamics. Parameters of the control are suboptimally selected by maximizing the stable region in the sense of Lyapunov with the aid of a genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.
Keywords: Augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1726115 Design of an Augmented Automatic Choosing Control by Lyapunov Functions Using Gradient Optimization Automatic Choosing Functions
Authors: Toshinori Nawata
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In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) using the gradient optimization automatic choosing functions for nonlinear systems. Constant terms which arise from sectionwise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics. Parameters included in the control are suboptimally selected by expanding a stable region in the sense of Lyapunov with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.Keywords: augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1495114 Controller Synthesis of Switched Positive Systems with Bounded Time-Varying Delays
Authors: Xinhui Wang, Xiuyong Ding
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This paper addresses the controller synthesis problem of discrete-time switched positive systems with bounded time-varying delays. Based on the switched copositive Lyapunov function approach, some necessary and sufficient conditions for the existence of state-feedback controller are presented as a set of linear programming and linear matrix inequality problems, hence easy to be verified. Another advantage is that the state-feedback law is independent on time-varying delays and initial conditions. A numerical example is provided to illustrate the effectiveness and feasibility of the developed controller.
Keywords: Switched copositive Lyapunov functions, positive linear systems, switched systems, time-varying delays, stabilization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1431113 Exponential Stability of Uncertain Takagi-Sugeno Fuzzy Hopfield Neural Networks with Time Delays
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In this paper, based on linear matrix inequality (LMI), by using Lyapunov functional theory, the exponential stability criterion is obtained for a class of uncertain Takagi-Sugeno fuzzy Hopfield neural networks (TSFHNNs) with time delays. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, these techniques lead to generalized and less conservative stability condition that guarantee the wide stability region. Finally, an example is given to illustrate our results by using MATLAB LMI toolbox.
Keywords: Hopfield neural network, linear matrix inequality, exponential stability, time delay, T-S fuzzy model.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1498112 Nonlinear Controller for Fuzzy Model of Double Inverted Pendulums
Authors: I. Zamani, M. H. Zarif
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In this paper a method for designing of nonlinear controller for a fuzzy model of Double Inverted Pendulum is proposed. This system can be considered as a fuzzy large-scale system that includes offset terms and disturbance in each subsystem. Offset terms are deterministic and disturbances are satisfied a matching condition that is mentioned in the paper. Based on Lyapunov theorem, a nonlinear controller is designed for this fuzzy system (as a model reference base) which is simple in computation and guarantees stability. This idea can be used for other fuzzy large- scale systems that include more subsystems Finally, the results are shown.
Keywords: Controller, Fuzzy Double Inverted Pendulums, Fuzzy Large-Scale Systems, Lyapunov Stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2506111 Existence and Globally Exponential Stability of Equilibrium for BAM Neural Networks with Mixed Delays and Impulses
Authors: Xiaomei Wang, Shouming Zhong
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In this paper, a class of generalized bi-directional associative memory (BAM) neural networks with mixed delays is investigated. On the basis of Lyapunov stability theory and contraction mapping theorem, some new sufficient conditions are established for the existence and uniqueness and globally exponential stability of equilibrium, which generalize and improve the previously known results. One example is given to show the feasibility and effectiveness of our results.
Keywords: Bi-directional associative memory (BAM) neural networks, mixed delays, Lyapunov stability theory, contraction mapping theorem, existence, equilibrium, globally exponential stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1474110 Chaotic Properties of Hemodynamic Responsein Functional Near Infrared Spectroscopic Measurement of Brain Activity
Authors: Ni Ni Soe , Masahiro Nakagawa
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Functional near infrared spectroscopy (fNIRS) is a practical non-invasive optical technique to detect characteristic of hemoglobin density dynamics response during functional activation of the cerebral cortex. In this paper, fNIRS measurements were made in the area of motor cortex from C4 position according to international 10-20 system. Three subjects, aged 23 - 30 years, were participated in the experiment. The aim of this paper was to evaluate the effects of different motor activation tasks of the hemoglobin density dynamics of fNIRS signal. The chaotic concept based on deterministic dynamics is an important feature in biological signal analysis. This paper employs the chaotic properties which is a novel method of nonlinear analysis, to analyze and to quantify the chaotic property in the time series of the hemoglobin dynamics of the various motor imagery tasks of fNIRS signal. Usually, hemoglobin density in the human brain cortex is found to change slowly in time. An inevitable noise caused by various factors is to be included in a signal. So, principle component analysis method (PCA) is utilized to remove high frequency component. The phase pace is reconstructed and evaluated the Lyapunov spectrum, and Lyapunov dimensions. From the experimental results, it can be conclude that the signals measured by fNIRS are chaotic.Keywords: Chaos, hemoglobin, Lyapunov spectrum, motorimagery, near infrared spectroscopy (NIRS), principal componentanalysis (PCA).
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1719109 Exponential Stability of Periodic Solutions in Inertial Neural Networks with Unbounded Delay
Authors: Yunquan Ke, Chunfang Miao
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In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of periodic solutions of the system are obtained. Finally, two examples are given to illustrate the effectiveness of the results.
Keywords: Inertial neural networks, unbounded delay, fixed-point theorem, Lyapunov function, periodic solutions, exponential stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1522108 An Augmented Automatic Choosing Control Designed by Extremizing a Combination of Hamiltonian and Lyapunov Functions for Nonlinear Systems with Constrained Input
Authors: Toshinori Nawata, Hitoshi Takata
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In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) for nonlinear systems with constrained input. Constant terms which arise from section wise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics.Parameters included in the control are suboptimally selectedby extremizing a combination of Hamiltonian and Lyapunov functions with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.
Keywords: Augmented Automatic Choosing Control, NonlinearControl, Genetic Algorithm, Hamiltonian, Lyapunovfunction
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1435107 Obstacle and Collision Avoidance Control Laws of a Swarm of Boids
Authors: Bibhya Sharma, Jito Vanualailai, Jai Raj
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This paper proposes a new obstacle and collision avoidance control laws for a three-dimensional swarm of boids. The swarm exhibit collective emergent behaviors whilst avoiding the obstacles in the workspace. While flocking, animals group up in order to do various tasks and even a greater chance of evading predators. A generalized algorithms for attraction to the centroid, inter-individual swarm avoidance and obstacle avoidance is designed in this paper. We present a set of new continuous time-invariant velocity control laws is presented which is formulated via the Lyapunov-based control scheme. The control laws proposed in this paper also ensures practical stability of the system. The effectiveness of the proposed control laws is demonstrated via computer simulations
Keywords: Lyapunov-based Control Scheme, Motion planning, Practical stability, Swarm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2485106 The First Integral Approach in Stability Problem of Large Scale Nonlinear Dynamical Systems
Authors: M. Kidouche, H. Habbi, M. Zelmat, S. Grouni
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In analyzing large scale nonlinear dynamical systems, it is often desirable to treat the overall system as a collection of interconnected subsystems. Solutions properties of the large scale system are then deduced from the solution properties of the individual subsystems and the nature of the interconnections. In this paper a new approach is proposed for the stability analysis of large scale systems, which is based upon the concept of vector Lyapunov functions and the decomposition methods. The present results make use of graph theoretic decomposition techniques in which the overall system is partitioned into a hierarchy of strongly connected components. We show then, that under very reasonable assumptions, the overall system is stable once the strongly connected subsystems are stables. Finally an example is given to illustrate the constructive methodology proposed.Keywords: Comparison principle, First integral, Large scale system, Lyapunov stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1515105 On the Robust Stability of Homogeneous Perturbed Large-Scale Bilinear Systems with Time Delays and Constrained Inputs
Authors: Chien-Hua Lee, Cheng-Yi Chen
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The stability test problem for homogeneous large-scale perturbed bilinear time-delay systems subjected to constrained inputs is considered in this paper. Both nonlinear uncertainties and interval systems are discussed. By utilizing the Lyapunove equation approach associated with linear algebraic techniques, several delay-independent criteria are presented to guarantee the robust stability of the overall systems. The main feature of the presented results is that although the Lyapunov stability theorem is used, they do not involve any Lyapunov equation which may be unsolvable. Furthermore, it is seen the proposed schemes can be applied to solve the stability analysis problem of large-scale time-delay systems.
Keywords: homogeneous bilinear system, constrained input, time-delay, uncertainty, transient response, decay rate.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1601104 Design of Adaptive Sliding Mode Controller for Robotic Manipulators Tracking Control
Authors: T. C. Kuo, Y. J. Huang, B. W. Hong
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This paper proposes an adaptive sliding mode controller which combines adaptive control and sliding mode control to control a nonlinear robotic manipulator with uncertain parameters. We use an adaptive algorithm based on the concept of sliding mode control to alleviate the chattering phenomenon of control input. Adaptive laws are developed to obtain the gain of switching input and the boundary layer parameters. The stability and convergence of the robotic manipulator control system are guaranteed by applying the Lyapunov theorem. Simulation results demonstrate that the chattering of control input can be alleviated effectively. The proposed controller scheme can assure robustness against a large class of uncertainties and achieve good trajectory tracking performance.Keywords: Robotic manipulators, sliding mode control, adaptive law, Lyapunov theorem, robustness.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3036103 Sliding Mode Control of Autonomous Underwater Vehicles
Authors: Ahmad Forouzan Tabar, Mohammad Azadi, Alireza Alesaadi
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This paper describes a sliding mode controller for autonomous underwater vehicles (AUVs). The dynamic of AUV model is highly nonlinear because of many factors, such as hydrodynamic drag, damping, and lift forces, Coriolis and centripetal forces, gravity and buoyancy forces, as well as forces from thruster. To address these difficulties, a nonlinear sliding mode controller is designed to approximate the nonlinear dynamics of AUV and improve trajectory tracking. Moreover, the proposed controller can profoundly attenuate the effects of uncertainties and external disturbances in the closed-loop system. Using the Lyapunov theory the boundedness of AUV tracking errors and the stability of the proposed control system are also guaranteed. Numerical simulation studies of an AUV are included to illustrate the effectiveness of the presented approach.
Keywords: Lyapunov stability, autonomous underwater vehicle (AUV), sliding mode controller, electronics engineering.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2581102 Robust Stability Criteria for Uncertain Genetic Regulatory Networks with Time-Varying Delays
Authors: Wenqin Wang, Shouming Zhong
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This paper presents the robust stability criteria for uncertain genetic regulatory networks with time-varying delays. One key point of the criterion is that the decomposition of the matrix ˜D into ˜D = ˜D1 + ˜D2. This decomposition corresponds to a decomposition of the delayed terms into two groups: the stabilizing ones and the destabilizing ones. This technique enables one to take the stabilizing effect of part of the delayed terms into account. Meanwhile, by choosing an appropriate new Lyapunov functional, a new delay-dependent stability criteria is obtained and formulated in terms of linear matrix inequalities (LMIs). Finally, numerical examples are presented to illustrate the effectiveness of the theoretical results.
Keywords: Genetic regulatory network, Time-varying delay, Uncertain system, Lyapunov-Krasovskii functional
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1519101 Stability Analysis of a Human-Mosquito Model of Malaria with Infective Immigrants
Authors: Nisha Budhwar, Sunita Daniel
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In this paper, we analyse the stability of the SEIR model of malaria with infective immigrants which was recently formulated by the authors. The model consists of an SEIR model for the human population and SI Model for the mosquitoes. Susceptible humans become infected after they are bitten by infectious mosquitoes and move on to the Exposed, Infected and Recovered classes respectively. The susceptible mosquito becomes infected after biting an infected person and remains infected till death. We calculate the reproduction number R0 using the next generation method and then discuss about the stability of the equilibrium points. We use the Lyapunov function to show the global stability of the equilibrium points.Keywords: Susceptible, exposed, infective, recovered, infective immigrants, reproduction number, Lyapunov function, equilibrium points, global stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1278100 Global Chaos Synchronization of Identical and Nonidentical Chaotic Systems Using Only Two Nonlinear Controllers
Authors: Azizan Bin Saaban, Adyda Binti Ibrahim, Mohammad Shehzad, Israr Ahmad
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In chaos synchronization, the main goal is to design such controller(s) that synchronizes the states of master and slave system asymptotically globally. This paper studied and investigated the synchronization problem of two identical Chen, and identical Tigan chaotic systems and two non-identical Chen and Tigan chaotic systems using Non-linear active control algorithm. In this study, based on Lyapunov stability theory and using non-linear active control algorithm, it has been shown that the proposed schemes have excellent transient performance using only two nonlinear controllers and have shown analytically as well as graphically that synchronization is asymptotically globally stable.
Keywords: Nonlinear Active Control, Chen and Tigan Chaotic systems, Lyapunov Stability theory, Synchronization.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 194899 Switching Rule for the Exponential Stability and Stabilization of Switched Linear Systems with Interval Time-varying Delays
Authors: Kreangkri Ratchagit
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This paper is concerned with exponential stability and stabilization of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton-s formula, a switching rule for the exponential stability and stabilization of switched linear systems with interval time-varying delays and new delay-dependent sufficient conditions for the exponential stability and stabilization of the systems are first established in terms of LMIs. Numerical examples are included to illustrate the effectiveness of the results.
Keywords: Switching design, exponential stability and stabilization, switched linear systems, interval delay, Lyapunov function, linear matrix inequalities.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 151498 The Decentralized Nonlinear Controller of Robot Manipulator with External Load Compensation
Authors: Sun Lim, Il-Kyun Jung
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This paper describes a newly designed decentralized nonlinear control strategy to control a robot manipulator. Based on the concept of the nonlinear state feedback theory and decentralized concept is developed to improve the drawbacks in previous works concerned with complicate intelligent control and low cost effective sensor. The control methodology is derived in the sense of Lyapunov theorem so that the stability of the control system is guaranteed. The decentralized algorithm does not require other joint angle and velocity information. Individual Joint controller is implemented using a digital processor with nearly actuator to make it possible to achieve good dynamics and modular. Computer simulation result has been conducted to validate the effectiveness of the proposed control scheme under the occurrence of possible uncertainties and different reference trajectories. The merit of the proposed control system is indicated in comparison with a classical control system.Keywords: Robot manipulator control, nonlinear controller, Lyapunov based stability, Interconnection compensation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 161797 Eukaryotic Gene Prediction by an Investigation of Nonlinear Dynamical Modeling Techniques on EIIP Coded Sequences
Authors: Mai S. Mabrouk, Nahed H. Solouma, Abou-Bakr M. Youssef, Yasser M. Kadah
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Many digital signal processing, techniques have been used to automatically distinguish protein coding regions (exons) from non-coding regions (introns) in DNA sequences. In this work, we have characterized these sequences according to their nonlinear dynamical features such as moment invariants, correlation dimension, and largest Lyapunov exponent estimates. We have applied our model to a number of real sequences encoded into a time series using EIIP sequence indicators. In order to discriminate between coding and non coding DNA regions, the phase space trajectory was first reconstructed for coding and non-coding regions. Nonlinear dynamical features are extracted from those regions and used to investigate a difference between them. Our results indicate that the nonlinear dynamical characteristics have yielded significant differences between coding (CR) and non-coding regions (NCR) in DNA sequences. Finally, the classifier is tested on real genes where coding and non-coding regions are well known.
Keywords: Gene prediction, nonlinear dynamics, correlation dimension, Lyapunov exponent.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 180896 Methodology for Quantifying the Meaning of Information in Biological Systems
Authors: Richard L. Summers
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The advanced computational analysis of biological systems is becoming increasingly dependent upon an understanding of the information-theoretic structure of the materials, energy and interactive processes that comprise those systems. The stability and survival of these living systems is fundamentally contingent upon their ability to acquire and process the meaning of information concerning the physical state of its biological continuum (biocontinuum). The drive for adaptive system reconciliation of a divergence from steady state within this biocontinuum can be described by an information metric-based formulation of the process for actionable knowledge acquisition that incorporates the axiomatic inference of Kullback-Leibler information minimization driven by survival replicator dynamics. If the mathematical expression of this process is the Lagrangian integrand for any change within the biocontinuum then it can also be considered as an action functional for the living system. In the direct method of Lyapunov, such a summarizing mathematical formulation of global system behavior based on the driving forces of energy currents and constraints within the system can serve as a platform for the analysis of stability. As the system evolves in time in response to biocontinuum perturbations, the summarizing function then conveys information about its overall stability. This stability information portends survival and therefore has absolute existential meaning for the living system. The first derivative of the Lyapunov energy information function will have a negative trajectory toward a system steady state if the driving force is dissipating. By contrast, system instability leading to system dissolution will have a positive trajectory. The direction and magnitude of the vector for the trajectory then serves as a quantifiable signature of the meaning associated with the living system’s stability information, homeostasis and survival potential.
Keywords: Semiotic meaning, Shannon information, Lyapunov, living systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 49295 Delay-dependent Stability Analysis for Uncertain Switched Neutral System
Authors: Lianglin Xiong, Shouming Zhong, Mao Ye
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This paper considers the robust exponential stability issues for a class of uncertain switched neutral system which delays switched according to the switching rule. The system under consideration includes both stable and unstable subsystems. The uncertainties considered in this paper are norm bounded, and possibly time varying. Based on multiple Lyapunov functional approach and dwell-time technique, the time-dependent switching rule is designed depend on the so-called average dwell time of stable subsystems as well as the ratio of the total activation time of stable subsystems and unstable subsystems. It is shown that by suitably controlling the switching between the stable and unstable modes, the robust stabilization of the switched uncertain neutral systems can be achieved. Two simulation examples are given to demonstrate the effectiveness of the proposed method.
Keywords: Switched neutral system, exponential stability, multiple Lyapunov functional, dwell time technique, time-dependent switching rule.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 138694 Nonlinear Dynamical Characterization of Heart Rate Variability Time Series of Meditation
Authors: B. S. Raghavendra, D. Narayana Dutt
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Many recent electrophysiological studies have revealed the importance of investigating meditation state in order to achieve an increased understanding of autonomous control of cardiovascular functions. In this paper, we characterize heart rate variability (HRV) time series acquired during meditation using nonlinear dynamical parameters. We have computed minimum embedding dimension (MED), correlation dimension (CD), largest Lyapunov exponent (LLE), and nonlinearity scores (NLS) from HRV time series of eight Chi and four Kundalini meditation practitioners. The pre-meditation state has been used as a baseline (control) state to compare the estimated parameters. The chaotic nature of HRV during both pre-meditation and meditation is confirmed by MED. The meditation state showed a significant decrease in the value of CD and increase in the value of LLE of HRV, in comparison with premeditation state, indicating a less complex and less predictable nature of HRV. In addition, it was shown that the HRV of meditation state is having highest NLS than pre-meditation state. The study indicated highly nonlinear dynamic nature of cardiac states as revealed by HRV during meditation state, rather considering it as a quiescent state.Keywords: Correlation dimension, Embedding dimension, Heartrate variability, Largest Lyapunov exponent, Meditation, Nonlinearity score.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 189793 Evolved Bat Algorithm Based Adaptive Fuzzy Sliding Mode Control with LMI Criterion
Authors: P.-W. Tsai, C.-Y. Chen, C.-W. Chen
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In this paper, the stability analysis of a GA-Based adaptive fuzzy sliding model controller for a nonlinear system is discussed. First, a nonlinear plant is well-approximated and described with a reference model and a fuzzy model, both involving FLC rules. Then, FLC rules and the consequent parameter are decided on via an Evolved Bat Algorithm (EBA). After this, we guarantee a new tracking performance inequality for the control system. The tracking problem is characterized to solve an eigenvalue problem (EVP). Next, an adaptive fuzzy sliding model controller (AFSMC) is proposed to stabilize the system so as to achieve good control performance. Lyapunov’s direct method can be used to ensure the stability of the nonlinear system. It is shown that the stability analysis can reduce nonlinear systems into a linear matrix inequality (LMI) problem. Finally, a numerical simulation is provided to demonstrate the control methodology.
Keywords: Adaptive fuzzy sliding mode control, Lyapunov direct method, swarm intelligence, evolved bat algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 205892 Discontinuous Galerkin Method for Total Variation Minimization on Inpainting Problem
Authors: Xijian Wang
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This paper is concerned with the numerical minimization of energy functionals in BV ( ) (the space of bounded variation functions) involving total variation for gray-scale 1-dimensional inpainting problem. Applications are shown by finite element method and discontinuous Galerkin method for total variation minimization. We include the numerical examples which show the different recovery image by these two methods.Keywords: finite element method, discontinuous Galerkin method, total variation minimization, inpainting
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 133191 Tracking Performance Evaluation of Robust Back-Stepping Control Design for a Nonlinear Electrohydraulic Servo System
Authors: M. Ahmadnezhad, M. Soltanpour
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Electrohydraulic servo system have been used in industry in a wide number of applications. Its dynamics are highly nonlinear and also have large extent of model uncertainties and external disturbances. In this paper, a robust back-stepping control (RBSC) scheme is proposed to overcome the problem of disturbances and system uncertainties effectively and to improve the tracking performance of EHS systems. In order to implement the proposed control scheme, the system uncertainties in EHS systems are considered as total leakage coefficient and effective oil volume. In addition, in order to obtain the virtual controls for stabilizing system, the update rule for the system uncertainty term is induced by the Lyapunov control function (LCF). To verify the performance and robustness of the proposed control system, computer simulation of the proposed control system using Matlab/Simulink Software is executed. From the computer simulation, it was found that the RBSC system produces the desired tracking performance and has robustness to the disturbances and system uncertainties of EHS systems.
Keywords: Electro hydraulic servo system, back-stepping control, robust back-stepping control, Lyapunov redesign
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2018